Question

Advertising medium Agency Increase Newspaper 1 $24.39 Newspaper 1 $22.68 Newspaper 1 $22.67 Newspaper 1 $23.95 Newspaper 1 $22.33 Newspaper 2 $22.25 Newspaper 2 $22.50 Newspaper 2 $25.61 Newspaper 2 $21.31 Newspaper 2 $24.40 Radio 1 $27.56 Radio 1 $20.35 Radio 1 $24.12 Radio 1 $22.98 Radio 1 $24.32 Radio 2 $23.35 Radio 2 $20.68 Radio 2 $27.12 Radio 2 $20.11 Radio 2 $25.50 Television 1 $26.64 Television 1 $22.91 Television 1 $24.84 Television 1 $25.07 Television 1 $28.58 Television 2 $23.51 Television 2 $26.03 Television 2 $27.24 Television 2 $24.15 Television 2 $22.09 Website 1 $24.41 Website 1 $24.21 Website 1 $26.88 Website 1 $27.58 Website 1 $25.81 Website 2 $27.02 Website 2 $30.16 Website 2 $29.56 Website 2 $32.45 Website 2 $29.21

A commuter airline wants to determine the combination of advertising medium (four levels) and advertising agency (two levels) that would produce the largest increase in ticket sales per advertising dollar spent. Each of the two advertising agencies has prepared advertisements in formats required for distribution by each of the media (including television, radio, newspaper, and Web site). Forty small towns of roughly the same size have been selected for this experiment. Furthermore, groups of five of these small towns have been assigned to receive an advertisement prepared and distributed by each of the eight agency–medium combinations. The dollar increases in ticket sales per advertising dollar spent, based on a one-month period, are listed in the file P19_36.xlsx. Test for any significant main effects and interactions at the 5% level, and briefly summarize your results.

Answer 1

Solution:

Here, we have to use the two way ANOVA or analysis of variance for checking the significant differences between different treatments and levels. Also, we have to check the hypothesis regarding the interaction between the two variables advertising medium and agency. The null and alternative hypotheses for this two way ANOVA are summarized as below:

Null hypothesis: H₀: There is no any significant difference in the increase in ticket sales per advertising dollar spent due to four different advertising mediums.

Alternative hypothesis: H_a: There is a statistically significant difference in the increase in ticket sales per advertising dollar spent due to four different advertising mediums.

Null hypothesis: H₀: There is no any significant difference in the increase in ticket sales per advertising dollar spent due to two different agencies.

Alternative hypothesis: H_a: There is a statistically significant difference in the increase in ticket sales per advertising dollar spent due to two different agencies.

Null hypothesis: H₀: There is no any statistically significant interaction between the two variables advertising medium and agency.

Alternative hypothesis: H_a: There is a statistically significant interaction between the two variables advertising medium and agency.

The descriptive statistics and ANOVA table for these tests are given as below:

We assume 5% level of significance or alpha value 0.05 for this analysis. From above ANOVA, it is observed that the p-value for the source advertising medium is given as 0.00 which is less than alpha value 0.05, so we reject the null hypothesis that there is no any significant difference in the increase in ticket sales per advertising dollar spent due to four different advertising mediums. There is sufficient evidence to conclude that there is a statistically significant difference in the increase in ticket sales per advertising dollar spent due to four different advertising mediums.

The p-value for the source agency is given as 0.369 which is greater than alpha value 0.05, so do not reject the null hypothesis that there is no any significant difference in the increase in ticket sales per advertising dollar spent due to two different agencies. There is insufficient evidence to conclude that there is a statistically significant difference in the increase in ticket sales per advertising dollar spent due to two different agencies.

The p-value for interaction between two variables advertising medium and agency is given as 0.049 which is less than alpha value 0.05, so we reject the null hypothesis that there is no any statistically significant interaction between the two variables advertising medium and agency. There is sufficient evidence to conclude that there is a statistically significant interaction between the two variables advertising medium and agency.